The dark matter halos that surround Milky Way-like galaxies in cosmological simulations are, to first order, triaxial. Nearly 30 years ago it was predicted that such triaxial dark matter halos should exhibit steady figure rotation or tumbling motions for durations of several gigayears. The angular frequency of figure rotation predicted by cosmological simulations is described by a log-normal distribution of pattern speed with a median value 0.15hkm/s/kpc (~ 0.15h rad/Gyr ~ 9h deg/Gyr) and a width of 0.83km/s/kpc. These pattern speeds are so small that they have generally been considered both unimportant and undetectable. In this work we show that even this extremely slow figure rotation can significantly alter the structure of extended stellar streams produced by the tidal disruption of satellites in the Milky Way halo. We simulate the behavior of a Sagittarius-like polar tidal stream in triaxial dark matter halos with different shapes, when the halos are rotated about the three principal axes. For pattern speeds typical of cosmological halos we demonstrate, for the first time, that a Sagittarius-like tidal stream would be altered to a degree that is detectable even with current observations. This discovery will potentially allow for a future measurement of figure rotation of the Milky Ways dark halo, and perhaps enabling the first evidence of this relatively unexplored prediction of LambdaCDM.
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